Year: 2026
Type: preprint
Abstract: In this paper, we establish spreading speeds for a nonlocal Fisher-KPP equation with measurable time-dependent asymmetric kernels, without imposing an inequality between growth and diffusion or requiring the kernel to be positive near the origin. The kernel has a time independent upper bound which is thin-tailed. Both the kernel and the linear growth rate have uniform means. Under these assumptions, we determine the exact rightward and leftward spreading speeds and prove convergence to the positive equilibrium inside the spreading interval. The proof is based on comparison arguments and a family of compactly supported subsolutions. Explicit examples show that time-dependent dispersal kernels with the same time average can exhibit different propagation behaviors.
Source: arXiv (Cornell University)
Authors: Jin, Zhucheng, Zhou, Tao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164892704